The different kinds of shapes in math

Written by catherine copeland
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The different kinds of shapes in math
Hexagons are a common shape studied in math. (Hemera Technologies/ Images)

Geometry classes cover the study of shapes. Students study different types of shapes in the different grade levels, eventually calculating their areas and perimeters. As students are promoted higher through the grade levels, they will study increasingly difficult and more complex shapes, often using a coordinate plane. The study of shapes is an ongoing process in higher math classes. The properties of triangles, for instance, are the basis of trigonometry.


A quadrilateral has four sides. The most common and basic quadrilateral is the square -- a four-sided figure with equal sides whose angles add up to 360 degrees. Other examples of quadrilaterals include rectangles, parallelograms, rhombuses, trapezoids and kites. A rectangle has four right angles. A rhombus is a parallelogram with all sides having equal length. Two of the trapezoid's four sides are parallel. Students often begin their studies of geometry with quadrilaterals, but these shapes will continue to make appearances during the coming school years.


Students will learn about triangles in beginning geometry, and will study them thoroughly in trigonometry. A triangle is a three-sided polygon whose interior angles add up to 180 degrees. The types of triangles include equilateral, scalene, obtuse, right and isosceles triangles. An equilateral triangle has all sides of the same length. In a scalene triangle, all sides are different lengths. An obtuse triangle has an angle greater than 90 degrees, while an acute triangle's angles are all less than 90 degrees.

Other Polygons

A polygon is a figure closed in an all sides by connecting line segments. These include quadrilaterals and triangles. Other polygons, however, have more than four sides. Common polygons include the pentagon, with five sides; the hexagon, six sides; the heptagon, seven sides; and the octagon, with eight sides. In a regular polygon, all sides are of the same length, while the sides of an irregular polygon are not the same length.


While it is a simple shape for beginning math students, it is a complex shape to study in later years. A circle is defined as a set of points on a plane that are all the same distance from a fixed point. A circle has no line segments or sides. Circles are often studied by a diameter and a radius. The properties of circles include the number pi. Pi, approximated as 3.14, represents the relationship between a circle's diameter and its circumference. The diameter is the width of a circle, and circumference is the distance around a circle.

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